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<div class="title">CDRSolver.py</div>  </div>
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<div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">#!/usr/bin/python</span>
<a name="l00002"></a>00002 <span class="comment"># -*- coding: utf-8 -*-</span>
<a name="l00003"></a>00003 
<a name="l00004"></a>00004 <span class="comment"># Copyright (c) 2011</span>
<a name="l00005"></a>00005 <span class="comment">#</span>
<a name="l00006"></a>00006 <span class="comment"># Permission is hereby granted, free of charge, to any person obtaining a</span>
<a name="l00007"></a>00007 <span class="comment"># copy of this software and associated documentation files (the &quot;Software&quot;),</span>
<a name="l00008"></a>00008 <span class="comment"># to deal in the Software without restriction, including without limitation</span>
<a name="l00009"></a>00009 <span class="comment"># the rights to use, copy, modify, merge, publish, distribute, sublicense,</span>
<a name="l00010"></a>00010 <span class="comment"># and/or sell copies of the Software, and to permit persons to whom the</span>
<a name="l00011"></a>00011 <span class="comment"># Software is furnished to do so, subject to the following conditions:</span>
<a name="l00012"></a>00012 <span class="comment">#</span>
<a name="l00013"></a>00013 <span class="comment"># The above copyright notice and this permission notice shall be included in</span>
<a name="l00014"></a>00014 <span class="comment"># all copies or substantial portions of the Software.</span>
<a name="l00015"></a>00015 <span class="comment">#</span>
<a name="l00016"></a>00016 <span class="comment"># THE SOFTWARE IS PROVIDED &quot;AS IS&quot;, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR</span>
<a name="l00017"></a>00017 <span class="comment"># IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,</span>
<a name="l00018"></a>00018 <span class="comment"># FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE</span>
<a name="l00019"></a>00019 <span class="comment"># AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER</span>
<a name="l00020"></a>00020 <span class="comment"># LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,</span>
<a name="l00021"></a>00021 <span class="comment"># OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE</span>
<a name="l00022"></a>00022 <span class="comment"># SOFTWARE.</span>
<a name="l00023"></a>00023 <span class="comment">#</span>
<a name="l00024"></a>00024 <span class="comment"># Author: Jesus Carrero &lt;j.o.carrero@gmail.com&gt;</span>
<a name="l00025"></a>00025 <span class="comment"># Mountain View, CA</span>
<a name="l00026"></a>00026 <span class="comment">#</span>
<a name="l00027"></a>00027 
<a name="l00028"></a>00028 <span class="keyword">from</span> DynamicSolverBase <span class="keyword">import</span> DynamicSolverBase
<a name="l00029"></a>00029 
<a name="l00030"></a>00030 <span class="keyword">import</span> time
<a name="l00031"></a>00031 <span class="keyword">from</span> scipy <span class="keyword">import</span> asarray
<a name="l00032"></a>00032 <span class="keyword">from</span> SecondOrderStatic1D <span class="keyword">import</span> SecondOrderStatic1D
<a name="l00033"></a>00033 <span class="keyword">from</span> utils.ProjOperators <span class="keyword">import</span> ProjOnShapeFunctions
<a name="l00034"></a>00034 
<a name="l00035"></a>00035 
<a name="l00036"></a><a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html">00036</a> <span class="keyword">class </span><a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html">CDRSolver</a>(DynamicSolverBase):
<a name="l00037"></a>00037 
<a name="l00038"></a>00038     <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00039"></a>00039 <span class="stringliteral">    Convection diffusion reaction solver.</span>
<a name="l00040"></a>00040 <span class="stringliteral">    Finite element P1, P2, splines.</span>
<a name="l00041"></a>00041 <span class="stringliteral">    Not stabilize.</span>
<a name="l00042"></a>00042 <span class="stringliteral">    &quot;&quot;&quot;</span>
<a name="l00043"></a>00043 
<a name="l00044"></a>00044     __slots__ = [<span class="stringliteral">&#39;m_diags&#39;</span>, <span class="stringliteral">&#39;m_mass_bd&#39;</span>, <span class="stringliteral">&#39;m_stiff_bd&#39;</span>, <span class="stringliteral">&#39;m_sos&#39;</span>,
<a name="l00045"></a>00045                  <span class="stringliteral">&#39;m_pival&#39;</span>]
<a name="l00046"></a>00046 
<a name="l00047"></a><a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#a74f56a1bc1836b4b9705e8ae924c017a">00047</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#a74f56a1bc1836b4b9705e8ae924c017a">__init__</a>(self, nsegs, xleft, xright):
<a name="l00048"></a>00048         <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00049"></a>00049 <span class="stringliteral">      m_pival ~ initial condition (projected on fem space)</span>
<a name="l00050"></a>00050 <span class="stringliteral">    &quot;&quot;&quot;</span>
<a name="l00051"></a>00051 
<a name="l00052"></a>00052         (self.m_diags, self.<a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#af4853175840a75c2f7efafa78ca2f5c3">m_pival</a>) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00053"></a>00053         (self.m_mass_bd, self.m_stiff_bd) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00054"></a>00054 
<a name="l00055"></a>00055         DynamicSolverBase.__init__(self)
<a name="l00056"></a>00056         self.<a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#a944a6ae40af4423413611308dbefc333">m_sos</a> = SecondOrderStatic1D(nsegs, xleft, xright)
<a name="l00057"></a>00057 
<a name="l00058"></a>00058     <span class="keyword">def </span>__bd_operator(self, dxl, dxr):
<a name="l00059"></a>00059         <span class="stringliteral">&quot;&quot;&quot; boudary conditions &quot;&quot;&quot;</span>
<a name="l00060"></a>00060 
<a name="l00061"></a>00061         basis = self.m_sos.get_sfunc()
<a name="l00062"></a>00062 
<a name="l00063"></a>00063         diffu_mat = basis.get_grad_grad()
<a name="l00064"></a>00064         conv_mat = basis.get_grad_disp()
<a name="l00065"></a>00065         mass_mat = basis.get_mass_mat()
<a name="l00066"></a>00066         mass_left_bd = mass_mat[1, 0] * dxl
<a name="l00067"></a>00067         mass_right_bd = mass_mat[0, -1] * dxr
<a name="l00068"></a>00068         mass_at_bd = asarray([mass_left_bd, mass_right_bd])
<a name="l00069"></a>00069 
<a name="l00070"></a>00070         (d, c, r) = self.m_sos.get_pdecos()
<a name="l00071"></a>00071 
<a name="l00072"></a>00072         left_kmat = -d * diffu_mat[1, 0] / dxl + c * conv_mat[1, 0] + r \
<a name="l00073"></a>00073             * mass_left_bd
<a name="l00074"></a>00074         right_kmat = -d * diffu_mat[0, -1] / dxr + c * conv_mat[0, -1] \
<a name="l00075"></a>00075             + r * mass_right_bd
<a name="l00076"></a>00076         stiff_at_bd = asarray([left_kmat, right_kmat])
<a name="l00077"></a>00077 
<a name="l00078"></a>00078         <span class="keywordflow">if</span> 3 == basis.dof():
<a name="l00079"></a>00079             mass_left_bd = mass_mat[2, 0] * dxl
<a name="l00080"></a>00080             mass_right_bd = mass_mat[1, -1] * dxr
<a name="l00081"></a>00081             mass_at_bd = asarray([mass_at_bd[0], mass_right_bd,
<a name="l00082"></a>00082                                  mass_left_bd, mass_at_bd[-1]],
<a name="l00083"></a>00083                                  <span class="stringliteral">&#39;float64&#39;</span>)
<a name="l00084"></a>00084 
<a name="l00085"></a>00085             left_kmat = -d * diffu_mat[2, 0] / dxl + c * conv_mat[2, 0] \
<a name="l00086"></a>00086                 + r * mass_left_bd
<a name="l00087"></a>00087             right_kmat = -d * diffu_mat[1, -1] / dxr + c * conv_mat[1,
<a name="l00088"></a>00088                     -1] + r * mass_right_bd
<a name="l00089"></a>00089             stiff_at_bd = asarray([stiff_at_bd[0], right_kmat,
<a name="l00090"></a>00090                                   left_kmat, stiff_at_bd[-1]], <span class="stringliteral">&#39;float64&#39;</span>
<a name="l00091"></a>00091                                   )
<a name="l00092"></a>00092 
<a name="l00093"></a>00093         mass_at_bd = mass_at_bd.reshape((basis.dof() - 1, 2))
<a name="l00094"></a>00094         stiff_at_bd = stiff_at_bd.reshape((basis.dof() - 1, 2))
<a name="l00095"></a>00095         <span class="keywordflow">return</span> (mass_at_bd, stiff_at_bd)
<a name="l00096"></a>00096 
<a name="l00097"></a>00097     <span class="keyword">def </span>_time_step(self, mass_bd, stiff_bd, diags):
<a name="l00098"></a>00098         <span class="stringliteral">&quot;&quot;&quot; set up time stepper, time step and return final result. &quot;&quot;&quot;</span>
<a name="l00099"></a>00099 
<a name="l00100"></a>00100         grid = self.m_sos.get_mesh()
<a name="l00101"></a>00101         dlx = grid.getDx()
<a name="l00102"></a>00102 
<a name="l00103"></a>00103         (xleft, xright) = grid.getRange()
<a name="l00104"></a>00104         (bd_mass, bd_kmat) = self.<a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#ad8a41159cbde090ff56f77f6c7743520">__bd_operator</a>(dlx[0], dlx[-1])
<a name="l00105"></a>00105 
<a name="l00106"></a>00106         <span class="comment"># Initialize Time stepper.</span>
<a name="l00107"></a>00107 
<a name="l00108"></a>00108         tstepper = self.get_tstepper()
<a name="l00109"></a>00109         tstepper.set_boperators(bd_mass, bd_kmat)
<a name="l00110"></a>00110 
<a name="l00111"></a>00111         tstepper.set_xlxr(xleft, xright)
<a name="l00112"></a>00112         tstepper.set_ival(self.<a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#af4853175840a75c2f7efafa78ca2f5c3">m_pival</a>[1:-1])
<a name="l00113"></a>00113         tstepper.set_bcond(self.get_lbc(), self.get_rbc())
<a name="l00114"></a>00114 
<a name="l00115"></a>00115         tstepper.set_moperators(mass_bd, stiff_bd, diags)
<a name="l00116"></a>00116 
<a name="l00117"></a>00117         dof = self.m_sos.get_sfunc().dof()
<a name="l00118"></a>00118         <span class="keywordflow">if</span> 2 == dof:
<a name="l00119"></a>00119             tstepper.set_mat_attrib(3)
<a name="l00120"></a>00120         <span class="keywordflow">if</span> 3 == dof:
<a name="l00121"></a>00121             tstepper.set_mat_attrib(5)
<a name="l00122"></a>00122 
<a name="l00123"></a>00123         <span class="keywordflow">return</span> tstepper.step()
<a name="l00124"></a>00124 
<a name="l00125"></a><a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#a9a96d51e353d85284d9bec17e0c3b973">00125</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#a9a96d51e353d85284d9bec17e0c3b973">get_mesh</a>(self):
<a name="l00126"></a>00126         <span class="stringliteral">&quot;&quot;&quot; grid use to assemble matrices. &quot;&quot;&quot;</span>
<a name="l00127"></a>00127 
<a name="l00128"></a>00128         <span class="keywordflow">return</span> self.m_sos.get_mesh()
<a name="l00129"></a>00129 
<a name="l00130"></a>00130 
<a name="l00131"></a><a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#ab7ba919c6d9a911c71e1bb5bb1934d84">00131</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#ab7ba919c6d9a911c71e1bb5bb1934d84">get_sfunc</a>(self):
<a name="l00132"></a>00132         <span class="stringliteral">&quot;&quot;&quot; shape functions defining the finite element space. &quot;&quot;&quot;</span>
<a name="l00133"></a>00133 
<a name="l00134"></a>00134         <span class="keywordflow">return</span> self.m_sos.get_sfunc()
<a name="l00135"></a>00135 
<a name="l00136"></a><a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#a0ee7423a6f41c8d246df5d13e4494bbf">00136</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#a0ee7423a6f41c8d246df5d13e4494bbf">get_pival</a>(self):
<a name="l00137"></a>00137         <span class="stringliteral">&quot;&quot;&quot; get temporal solution.&quot;&quot;&quot;</span>
<a name="l00138"></a>00138 
<a name="l00139"></a>00139         <span class="keywordflow">return</span> self.<a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#af4853175840a75c2f7efafa78ca2f5c3">m_pival</a>[1:-1]
<a name="l00140"></a>00140 
<a name="l00141"></a><a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#ac362db72e28979b57400facd94f5b9fb">00141</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#ac362db72e28979b57400facd94f5b9fb">set_diffus_cos</a>(self, diff, conv, reac, d_is_real, c_is_real,
<a name="l00142"></a>00142             r_is_real):
<a name="l00143"></a>00143         <span class="stringliteral">&quot;&quot;&quot; set diffusion coefficients. &quot;&quot;&quot;</span>
<a name="l00144"></a>00144 
<a name="l00145"></a>00145         self.m_sos.set_cos(
<a name="l00146"></a>00146             diff,
<a name="l00147"></a>00147             conv,
<a name="l00148"></a>00148             reac,
<a name="l00149"></a>00149             d_is_real,
<a name="l00150"></a>00150             c_is_real,
<a name="l00151"></a>00151             r_is_real,
<a name="l00152"></a>00152             )
<a name="l00153"></a>00153 
<a name="l00154"></a><a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#ac48e2a5aba00449d99a0684bee60fdf5">00154</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#ac48e2a5aba00449d99a0684bee60fdf5">set_sfunc_and_quads</a>(self, shfunts, quad):
<a name="l00155"></a>00155         <span class="stringliteral">&quot;&quot;&quot; finite element space and quad formulas. &quot;&quot;&quot;</span>
<a name="l00156"></a>00156 
<a name="l00157"></a>00157         self.m_sos.set_sfunc_and_quads(shfunts, quad)
<a name="l00158"></a>00158 
<a name="l00159"></a><a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#a4f9806879a3c1744ba2de5fe6bbf8470">00159</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#a4f9806879a3c1744ba2de5fe6bbf8470">set_up_problem</a>(self):
<a name="l00160"></a>00160         <span class="stringliteral">&quot;&quot;&quot; Only Dirichlet bc are implemented.&quot;&quot;&quot;</span>
<a name="l00161"></a>00161 
<a name="l00162"></a>00162         start = time.time()
<a name="l00163"></a>00163         self.<a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#af4853175840a75c2f7efafa78ca2f5c3">m_pival</a> = ProjOnShapeFunctions(self.m_sos.get_sfunc(),
<a name="l00164"></a>00164                 self.m_sos.get_quads(), self.m_sos.get_mesh(),
<a name="l00165"></a>00165                 self.get_ivalf())
<a name="l00166"></a>00166 
<a name="l00167"></a>00167         <span class="comment"># *************************************************</span>
<a name="l00168"></a>00168 
<a name="l00169"></a>00169         dof = self.m_sos.get_sfunc().dof()
<a name="l00170"></a>00170         st_diag = self.m_sos.get_stiff_dformat()
<a name="l00171"></a>00171         ma_diag = self.m_sos.get_mass_dformat()
<a name="l00172"></a>00172 
<a name="l00173"></a>00173         <span class="keywordflow">if</span> 2 == dof:
<a name="l00174"></a>00174             stiff_bd = asarray([list(st_diag[1:-1, 0].flatten()),
<a name="l00175"></a>00175                                list(st_diag[1:-1, 1].flatten()),
<a name="l00176"></a>00176                                list(st_diag[1:-1, 2].flatten())])
<a name="l00177"></a>00177             mass_bd = asarray([list(ma_diag[1:-1, 0].flatten()),
<a name="l00178"></a>00178                               list(ma_diag[1:-1, 1].flatten()),
<a name="l00179"></a>00179                               list(ma_diag[1:-1, 2].flatten())])
<a name="l00180"></a>00180             diags = asarray([0, 1, -1])
<a name="l00181"></a>00181         <span class="keywordflow">if</span> 3 == dof:
<a name="l00182"></a>00182             stiff_bd = asarray([list(st_diag[1:-1, 0].flatten()),
<a name="l00183"></a>00183                                list(st_diag[1:-1, 1].flatten()),
<a name="l00184"></a>00184                                list(st_diag[1:-1, 2].flatten()),
<a name="l00185"></a>00185                                list(st_diag[1:-1, 3].flatten()),
<a name="l00186"></a>00186                                list(st_diag[1:-1, 4].flatten())])
<a name="l00187"></a>00187             mass_bd = asarray([list(ma_diag[1:-1, 0].flatten()),
<a name="l00188"></a>00188                               list(ma_diag[1:-1, 1].flatten()),
<a name="l00189"></a>00189                               list(ma_diag[1:-1, 2].flatten()),
<a name="l00190"></a>00190                               list(ma_diag[1:-1, 3].flatten()),
<a name="l00191"></a>00191                               list(ma_diag[1:-1, 4].flatten())])
<a name="l00192"></a>00192             diags = asarray([0, 1, -1, 2, -2])
<a name="l00193"></a>00193 
<a name="l00194"></a>00194         <span class="keywordflow">if</span> self.do_log():
<a name="l00195"></a>00195             self.log_info(<span class="stringliteral">&#39;&#39;</span>)
<a name="l00196"></a>00196             self.log_info(<span class="stringliteral">&#39;Assembling system takes &#39;</span> + str(time.time()
<a name="l00197"></a>00197                           - start) + <span class="stringliteral">&#39; secs&#39;</span>)
<a name="l00198"></a>00198 
<a name="l00199"></a>00199         (self.m_mass_bd, self.m_stiff_bd, self.m_diags) = (mass_bd,
<a name="l00200"></a>00200                 stiff_bd, diags)
<a name="l00201"></a>00201 
<a name="l00202"></a><a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#ad9d48ea2793fce123c909ff82253c92e">00202</a>     <span class="keyword">def </span><a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#ad9d48ea2793fce123c909ff82253c92e">solve</a>(self):
<a name="l00203"></a>00203         <span class="stringliteral">&quot;&quot;&quot; solve pde &quot;&quot;&quot;</span>
<a name="l00204"></a>00204 
<a name="l00205"></a>00205         <span class="keywordflow">if</span> <span class="keywordtype">None</span> == self.<a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#af4853175840a75c2f7efafa78ca2f5c3">m_pival</a>:
<a name="l00206"></a>00206             self.<a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#a4f9806879a3c1744ba2de5fe6bbf8470">set_up_problem</a>()
<a name="l00207"></a>00207 
<a name="l00208"></a>00208         <span class="keywordflow">return</span> self.<a class="code" href="classmodels_1_1CDRSolver_1_1CDRSolver.html#ae0c371bbc70648b41617771e4fb9b039">_time_step</a>(self.m_mass_bd, self.m_stiff_bd,
<a name="l00209"></a>00209                                self.m_diags)
<a name="l00210"></a>00210 
<a name="l00211"></a>00211 
</pre></div></div>
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